WASHINGTON -- Months of efforts by moderate Senate Republicans to effect a compromise with the White House on a civil rights bill are likely to give way this week to a test of congressional strength to override a presidential veto.

The Senate is scheduled to take up consideration of the bill at some time this week. But debate could conflict with the chamber's deliberations on whether to confirm Judge Clarence Thomas for a Supreme Court seat, which are also on the Senate docket for this week.

In any event, the dismissal last week by the White House of the most recent -- and possibly the last -- attempt to reach a compromise on the civil rights bill has increased the prospect of an eventual veto. There is an air of inevitability about a veto, which would bring on the showdown between Congress and President Bush.

Moreover, chances are growing that the bill, in the form of a debate over so-called racial quotas, will become a major issue in next year's presidential election. Almost lost in the debate is the original purpose of all the various versions of the civil rights bill: the repeal, in effect, of six Supreme Court decisions that the civil rights establishment regards as having diluted the nation's laws against racial discrimination.

Mr. Bush vetoed last year's proposed civil rights measure, calling it a "quota bill" that would have forced employers to hire minorities and women on a numerical basis to avoid anti-discrimination suits.

Last week, when the White House rejected the most recent of several compromise efforts by Sen. John C. Danforth of Missouri, leader of the moderate Republican compromise-seekers, the presidential spokesman, Marlin Fitzwater, was asked if the senators' proposals amounted to a "quota bill."

"That's never changed," Mr. Fitzwater replied. "You see," he added during a news briefing, "the basic problem here is [that] Ralph Neas and the Leadership Conference . . . want quotas and . . . they want a political issue and that's it."

The White House press secretary was referring to the executive director of the Leadership Conference on Civil Rights, the lobbying coalition of about 185 organizations which has been the prime force outside of Congress for enactment of a civil rights bill -- but in versions that the White House has never been able to accept.

"This is not a quota issue," Mr. Danforth responded from the Senate floor. "I am sorry that yet again this word 'quota' is being bandied about wrongly as a way to try to characterize this legislation."

The senator described any attempt to build a political issue on quotas as "race politics," which he said "is not only bad for my political party, I believe it's bad for the country."

Nevertheless, President Bush's campaign advisers obviously are aware that the "quota issue" worked last year to the benefit of the re-election of Republican Sen. Jesse Helms in a close contest in North Carolina and the election of Pete Wilson as the Republican governor of California.

Meanwhile, Mr. Danforth, as compromise-seeker and as Judge Thomas' chief Senate sponsor, is at the center of two of the major controversies of the day.

"Since Senator Danforth carried the water for you on Judge Thomas, don't you think you guys owe him one?" a reporter asked Mr. Fitzwater last week.

The White House spokesman acknowledged that the senator "has done an outstanding job" for the White House in sponsoring Judge Thomas, but he said that the civil rights bill was "a matter of very serious substantive content, and we simply disagree" about it.

Clint Bolick, a conservative attorney who is an ardent supporter of Judge Thomas and just as ardent an opponent of the civil rights bill, expressed certainty that in the White House and Congress, both issues "are being treated separately and on their merits."

But Washington has been full of accusations from each side of the issue that the other simply didn't want a bill. Mr. Fitzwater said that Mr. Neas and the Leadership Conference "don't want a bill." Mr. Neas said that the White House "does not want a civil rights bill enacted into law."

Mr. Danforth was asked if he believed that White House Chief of Staff John H. Sununu, who has been Mr. Bush's chief adviser on the issue of a civil rights bill, might not want a bill to be enacted. The senator, visibly angry at the White House rejection of his compromise proposal, merely responded, "That's possible."

Against this background, both sides have turned to talk of a Bush veto. Mr. Fitzwater insisted that the president still would "like to have a civil rights bill he can sign." But when asked if a veto could be sustained by both houses of Congress, he said that "we would certainly work to do that."

Mr. Danforth, on the other hand, said he would attempt to gain congressional approval of a civil rights bill by the two-thirds majority in each house that would be required to override a veto.

Last October, when the 100-member Senate sought to override Mr. Bush's veto of the 1990 civil rights bill, its tally of 66-34 came within one vote of securing the necessary two-thirds majority. All 55 Democrats and 11 of the 45 Republicans in the Senate at that time voted to override. This year, there are two more Democrats and two fewer Republicans in the Senate.

The 435-member House has already approved a civil rights bill this year, but on the basis of those members of the House who were present and voting, the tally fell 15 votes short of what would have been needed to override a veto.

The vote in June was 273-158 to pass a version of the bill later introduced in the Senate by Sen. Edward M. Kennedy, D-Mass. In that vote, 250 of the House's 267 Democrats and one independent voted for the bill, while 143 of the House's 167 Republicans voted against it.